Find the volume of the solid generated by rotating about the y-axis the region under the curve , from to .

Find the volume of the solid generated when the function

is revolved around the x-axis on the interval .

Hint: Use the method of cylindrical disks.

Find the area bound by the curve of g(t), the x and y axes, and the line

Approximate the volume of a solid in the first quadrant revolved about the y-axis and bounded by the functions: and . Round the volume to the nearest integer.

Suppose the functions , , and form a closed region. Rotate this region across the x-axis. What is the volume?

What is the volume of the solid formed when the line is rotated around the -axis from to ?

A man fills up a cup of water by leaving it outside during a rainstorm. The rate at which the height of the cup changes is equal to . What is the height of water at ? Assume the cup is empty at .

Determine the volume of the solid obtained by rotating the region with the following bounds about the x-axis:

Using the method of cylindrical disks, find the volume of the region revolved around the x-axis of the graph of

on the interval

Determine the volume of a solid created by rotating the curve and the line by revolving around the -axis.